Tightness for thick points in two dimensions

arxiv（2023）

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摘要

Let Wt be Brownian motion in the plane started at the origin and let & theta; be the first exit time of the unit disk D1. Let Z 0 1 & mu;0(x, ⠏) = 1{B(x,E)}(Wt) dt, & pi;⠏2 0 and set & mu;*0(⠏) = SUPx & ISIN;D1 & mu;0(x, ⠏). We show that � � � � & mu;* 0(⠏) - 2/& pi; log ⠏-1 - 2 1 log log ⠏-1 is tight.

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关键词

thick points,two dimensional sphere,barrier estimates

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